My invention refers to the need of either reducing or limiting, in the aforementioned elements and parts of equipment, the amplitude of oscillations induced on them by the vibrations specified. When these elements are parts are, on account of their nature, flexible and of only limited structural strength, they can not be dimensioned, either, to resist the maximal structural loads, or to accept the maximal displacements which may be induced on them, by the vibrations. This, on account of these elements representing an oscillator, in which their structural flexibility represents the elastic component, and their structural weight, the oscillating mass.
The energy introduced by the vibration begins to accumulate, in the oscillatory play between the kinetic energy acquired by the mass, and the potential energy, generated after a certain delay-characterized by the natural period of the oscillator-, by the elastic component. This oscillatory play continues to increase, until a state of equilibrium arrives, between the energy being introduced by the vibration, and the energy being dissipated, on account of the elastic hysteresis in the structural materials, and the friction which may be opposed to the movement of the mass. Both of these effects, jointly, represent the damping of the oscillator: if and when this damping is low enough, on account of the nature of the element, the oscillations could only be limited by introducing separate damping devices.
In the elements of the plants described above, the structural materials to be used (insulators, metal structures) are, indeed, frequently characterized, by their low energy absorption. Introducing vibration dampers into these elements may be, however, difficult: the dampers, to operate, need to detect the motion of the oscillator relative to the ground. But, in general, they can not be coupled to the maximum displacements of the elements (upper part of a column, middle part of a beam), and must be inserted, in the definite form of vibration isolators, between the element and its supports (base of a column, supporting ends of a beam). In these conditions, they introduce there, by nature, a considerable elasticity which, having been even welcomed, on occasions, as a distinct advantage, in most cases represents a serious difficulty, even an insuperable one, on account of the alterations which this flexibility may determine, on other functional characteristics of the element.
The design of the vibration isolators themselves, has been, moreover, strongly subdued on account of this location, and it has arrived that the isolators be self-defeating, on account of the displacements at other parts of the element, which result strongly amplified, as a geometrical consequence of the isolators' elasticity.
Former difficulties have called for a search to apply, to the elements and parts of the abovementioned plants, the already known principle of the dynamic vibration absorber, that means, a secondary oscillator fixed upon the element, in the zone of its maximal displacements, which transforms part of the energy in play, into dynamical reaction pulses, with a period somewhat different to that of the principle oscillator. If the ratios of the masses and of the periods are correct, the pulses will be adequate to alter the oscillatory play of energy within the principal oscillator: the "response" of this will not reach to the values it had, and the oscillations will be limited, by this dynamical effect, with a final result similar to what could have been obtained from an efficient set of vibration isolators.
By nature of this explanation itself, it may be feared that the dynamic absorber could only be operative if the values of its mass and its elasticity, are definitely determined for the principal oscillator involved, and then, only for periodical and permanent vibrations acting on. In other case, the pulses of the auxiliary mass could prove, at certain moments at least, self-defeating, and contributing more to increase the energy play, as to limit it.
The theory, however, establishes that this danger is overcome, by introducing into the secondary oscillator an adequate damping: this oscillator may be, in this case, considered as a device which pumps out of the principal oscillator, a part of the energy in play, to dissipate it within itself. An excessive value for this damping could, still, originate undue dynamical reactions, but the dynamical absorbing will be now effective, for a range of values of the mass and the elasticity of the auxiliary oscillator. Optimum effects could be obtained with masses between 10 and 20% of the principal one; natural frequencies within .+-.20% of the frequency of the principal oscillator, and auxiliary damping, between 10 and 20% of the critical.
If one intends to use a system of such auxiliary mass dampers with a standard design, even these values could be considered as demanding a too close matching to the element, for an adequate efficiency. It would be for the worse, if one considers that there is a certain interaction between these values, within these ranges, and the fact that the vibrations of interest are, by nature, irregular and transient.
There are, however, three more measures to be recurred at, to flatten the difficulties: (a) to fractionate the auxiliary mass into a quantity of small bodies or particles, so as to make its apparent frequency more the effect of a statistical behaviour, than a definite value; (b) to discard the elasticity of the auxiliary oscillator, leaving the mass to be restored by a means less well defined than that of a spring; (c) to eliminate the restoring effect for the mass, by having the auxiliary oscillator reduced to a "mass" with a "damper", but without any apparent "elasticity" (astatic oscillator. The three possibilities represent, in the end, the introduction of different types or grades of "non-linearity" into the auxiliary oscillator.